Hidden hamiltonians of first-order equations

L.J.F. Broer

Research output: Contribution to journalArticleAcademicpeer-review

8 Citations (Scopus)


There are equations, like the KDV equation, of which the solutions behave like conservative systems although the equation is of first order in time. It is shown how equations of this kind can originate by a direct-product like process of fusion of two canonical conjugate variables. Conversely, for a class of dynamically well-behaved first-order equations a splitting of the independent variable into two conjugate parts and a corresponding hamiltonian functional can be found. It is shown how the action principle and the Noether theorem transform during this fusion or splitting process. A number of examples are discussed. It is shown how a KDV approximation can be derived directly from the hamiltonian of a second-order system without using the second-order wave equations.
Original languageEnglish
Pages (from-to)583-596
JournalPhysica A: Statistical and Theoretical Physics
Issue number6
Publication statusPublished - 1975


Dive into the research topics of 'Hidden hamiltonians of first-order equations'. Together they form a unique fingerprint.

Cite this